Blender Cycles - Can't see Glass through Glass
I thank and praise the Lord Jesus Christ for answering prayer and showing me the solution!
The issue was not with the glass encasement material after all. Mixing between glass and transparent shaders based on shadow, diffuse, and glossy outputs from the Light Path node was correct. The problem was actually with the glass bulb and filament materials!
In the original setup for the glass bulb, a transparent shader was being mixed in TWICE (this essentially was the setup for architectural glass, minus the translucent shader with its mix node, as shown on BlenderGuru). However, the way the 2nd transparent shader was being mixed in (via light path node) was conflicting with the material's ability to be seen at full illumination THROUGH the outside beveled glass encasement.
Outside of the glass it looked fine, but inside, it's strength was being clamped. This was the same problem for the filament material, which was mixing in a transparent shader in the same way. The solution for the glass bulb material was to delete the 2nd transparent shader, and for the filament, it was to remove the transparent element completely.
New setups are shown below:



EDIT: I should note that I no longer add the &quot;glossy&quot; ray in the Light path node-- I only add shadow and diffuse together. If you add glossy, your glass object will not reflect in mirrors, which is a highly undesirable effect. :-)